Battery and Critical Mineral Recycling Act of 2021 This bill provides support to reuse and recycle batteries and the critical minerals contained in them. Specifically, the bill establishes incentives for reusing and recycling batteries, including by establishing three grant programs. It also requires the Department of Energy (DOE) to continue carrying out its Lithium-Ion Battery Recycling Prize competition. In addition, the bill establishes within DOE and the Environmental Protection Agency (EPA) a voluntary labeling program to improve battery collection and reduce battery waste. The EPA must also develop best practices for the collection of batteries that states and local governments may follow. Additionally, DOE must convene a task force to develop an extended battery producer responsibility framework that outlines regulatory pathways for effective recycling.